Examination of Factorization Ansatz of S-matrix in Massive Thirring Model

We examine the factorization ansatz of the S-matrix in the massive Thirring model. Using the rapidity values obtained numerically for the vacuum as well as for the 1p − 1h and the 2p − 2h states, we show that the factorization of the S-matrix for the particle hole scattering does not hold. This is because the crossing symmetry and the factorization do not commute with each other. This indicates that the soliton antisoliton S-matrix factorization picture of the sineGordon model is semiclassical and does not lead to a full quantization procedure of the massive Thirring model. Manuscript pages 26: Figures 3: Tables 3 e-mail: [email protected] e-mail: [email protected] 1 Proposed running head: ” S-matrix factorization for massive Thirring” Mailing Address: T. Fujita Department of Physics Faculty of Science and Technology Nihon University Kanda-Surugadai Tokyo, Japan Telephone: (03)3259-0887 (Japan) Fax: (03)3293-8269 (Japan) e-mail: [email protected]